Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
	import java.util.*;
	import java.math.*;
	public class abc {
	
		public static void main(String args[]) throws IOException {
	
					BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
					OutputStream out=new BufferedOutputStream(System.out);
					int n=Integer.parseInt(br.readLine());
					int ans=(int)(Math.ceil(((double)n-1.0)/2.0))+1;
					out.write((ans+"\n").getBytes());
					out.write("1 1\n".getBytes());
					int q =1;
					for(int i=2;i<=n;i++){
						while(1==1){
						int row=q/ans;
					   int col=q%ans;
//					   System.out.println((row+1)+" "+(col+1));
						if((row)+(col)<i-1){
							q++;
						}
						else{
							out.write(((row+1)+" "+(col+1)+"\n").getBytes());
							break;
						}
						}
					   
					}
					
					out.flush();
				}
			}